Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ The Wechsler Intelligence Scale for Children (WISC) is a test that is used clinically to assess the IQ of children between the ages of 6 and 16 years old. Scores on the WISC follow a normal distribution with a mean value of 100and a standard deviation of 15.

Children who score between 110 and 119 are considered "High Average" IQ. What percentage of all children fall in the "High Average" range?

To find the percentage of children in the "High Average" range on the WISC, we calculate the z-scores for scores of 110 and 119, resulting in approximately 14.9% of children falling into this category.

Explanation:

We want to determine what percentage of all children fall in the "High Average" IQ range on the Wechsler Intelligence Scale for Children (WISC), which classifies those with scores between 110 and 119 as "High Average." To find this percentage, we utilize the properties of the normal distribution under which the WISC scores fall. These scores have a mean (average) of 100 and a standard deviation of 15.

Since the normal distribution is symmetric, and IQ scores typically follow this pattern, we calculate the z-scores for both 110 and 119. The formula for a z-score is:

Z = (X - μ) / σ

where X is the score, μ (mu) is the mean, and σ (sigma) is the standard deviation. Thus:

For 110: Z = (110 - 100) / 15 ≈ 0.67
For 119: Z = (119 - 100) / 15 ≈ 1.27

Looking up these z-scores on a standard normal distribution table or using a calculator gives the percentages of people who score below each point. The percentage of children scoring below 110 is approximately 74.8%, and below 119 is approximately 89.7%. Therefore, the percentage of children falling in the "High Average" range is the difference between these two percentages, which is about 14.9%.